• Title/Summary/Keyword: finite group

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An Upper Bound for the Probability of Generating a Finite Nilpotent Group

  • Halimeh Madadi;Seyyed Majid Jafarian Amiri;Hojjat Rostami
    • Kyungpook Mathematical Journal
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    • v.63 no.2
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    • pp.167-173
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    • 2023
  • Let G be a finite group and let ν(G) be the probability that two randomly selected elements of G produce a nilpotent group. In this article we show that for every positive integer n > 0, there is a finite group G such that ${\nu}(G)={\frac{1}{n}}$. We also classify all groups G with ${\nu}(G)={\frac{1}{2}}$. Further, we prove that if G is a solvable nonnilpotent group of even order, then ${\nu}(G){\leq}{\frac{p+3}{4p}}$, where p is the smallest odd prime divisor of |G|, and that equality exists if and only if $\frac{G}{Z_{\infty}(G)}$ is isomorphic to the dihedral group of order 2p where Z(G) is the hypercenter of G. Finally we find an upper bound for ν(G) in terms of |G| where G ranges over all groups of odd square-free order.

COUNTING THE CINTRALIZERS OF SOME FINITE GROUPS

  • Ashrafi, Ali Reza
    • Journal of applied mathematics & informatics
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    • v.7 no.1
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    • pp.115-124
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    • 2000
  • For a finite group G, #Cent(G) denotes the number of cen-tralizers of its clements. A group G is called n-centralizer if #Cent( G) = n. and primitive n-centralizer if #Cent(G) = #Cent(${\frac}{G}{Z(G)$) = n. In this paper we compute the number of distinct centralizers of some finite groups and investigate the structure of finite groups with Qxactly SLX distinct centralizers. We prove that if G is a 6-centralizer group then ${\frac}{G}{Z(G)$${\cong}D_8$,$A_4$, $Z_2{\times}Z_2{\times}Z_2$ or $Z_2{\times}Z_2{\times}Z_2{\times}Z_2$.

THE KERNELS OF THE LINEAR MAPS OF FINITE GROUP ALGEBRAS

  • Dan Yan
    • Bulletin of the Korean Mathematical Society
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    • v.61 no.1
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    • pp.45-64
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    • 2024
  • Let G be a finite group, K a split field for G, and L a linear map from K[G] to K. In our paper, we first give sufficient and necessary conditions for Ker L and Ker L ∩ Z(K[G]), respectively, to be Mathieu-Zhao spaces for some linear maps L. Then we give equivalent conditions for Ker L to be Mathieu-Zhao spaces of K[G] in term of the degrees of irreducible representations of G over K if G is a finite Abelian group or G has a normal Sylow p-subgroup H and L are class functions of G/H. In particular, we classify all Mathieu-Zhao spaces of the finite Abelian group algebras if K is a split field for G.

Finite-element analysis of the center of resistance of the mandibular dentition

  • Jo, A-Ra;Mo, Sung-Seo;Lee, Kee-Joon;Sung, Sang-Jin;Chun, Youn-Sic
    • The korean journal of orthodontics
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    • v.47 no.1
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    • pp.21-30
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    • 2017
  • Objective: The aim of this study was to investigate the three-dimensional (3D) position of the center of resistance of 4 mandibular anterior teeth, 6 mandibular anterior teeth, and the complete mandibular dentition by using 3D finite-element analysis. Methods: Finite-element models included the complete mandibular dentition, periodontal ligament, and alveolar bone. The crowns of teeth in each group were fixed with buccal and lingual arch wires and lingual splint wires to minimize individual tooth movement and to evenly disperse the forces onto the teeth. Each group of teeth was subdivided into 0.5-mm intervals horizontally and vertically, and a force of 200 g was applied on each group. The center of resistance was defined as the point where the applied force induced parallel movement. Results: The center of resistance of the 4 mandibular anterior teeth group was 13.0 mm apical and 6.0 mm posterior, that of the 6 mandibular anterior teeth group was 13.5 mm apical and 8.5 mm posterior, and that of the complete mandibular dentition group was 13.5 mm apical and 25.0 mm posterior to the incisal edge of the mandibular central incisors. Conclusions: Finite-element analysis was useful in determining the 3D position of the center of resistance of the 4 mandibular anterior teeth group, 6 mandibular anterior teeth group, and complete mandibular dentition group.

ON PROJECTIVE REPRESENTATIONS OF A FINITE GROUP AND ITS SUBGROUPS I

  • Park, Seung-Ahn;Park, Eun-Mi
    • Journal of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.387-397
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    • 1996
  • Let G be a finite group and F be a field of characteristic $p \geq 0$. Let $\Gamma = F^f G$ be a twisted group algebra corresponding to a 2-cocycle $f \in Z^2(G,F^*), where F^* = F - {0}$ is the multiplicative subgroup of F.

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FINITE GROUP ACTIONS ON THE 3-DIMENSIONAL NILMANIFOLD

  • Goo, Daehwan;Shin, Joonkook
    • Journal of the Chungcheong Mathematical Society
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    • v.18 no.2
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    • pp.223-232
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    • 2005
  • We study only free actions of finite groups G on the 3-dimensional nilmanifold, up to topological conjugacy which yields an infra-nilmanifold of type 2.

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